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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks on Naimark's duality


Author: Wojciech Czaja
Journal: Proc. Amer. Math. Soc. 136 (2008), 867-871
MSC (2000): Primary 42C15
Published electronically: November 30, 2007
MathSciNet review: 2361858
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Abstract: We present an extension of a version of Naimark's dilation theorem which states that complete systems in a Hilbert space are projections of $ \omega$-linearly independent systems of elements of an ambient Hilbert space. This result is presented in the context of other known extensions of Naimark's theorem.


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Additional Information

Wojciech Czaja
Affiliation: Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Address at time of publication: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: wojtek@math.umd.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09048-X
PII: S 0002-9939(07)09048-X
Keywords: Naimark dilation theorem, frame, Bessel system, complete system, Riesz basis, representation system, Schauder basis, linearly independent system
Received by editor(s): January 3, 2005
Received by editor(s) in revised form: April 26, 2006
Published electronically: November 30, 2007
Additional Notes: The author was supported by Marie Curie Intra-European Fellowship FP6-2003-500685
Communicated by: David R. Larson
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.